Is it possible to integrate the GPT-3 by OpenAPI inside Unity3D or any game-engine?
Yes, OpenAI will release an API for GPT-3, so any developer can integrate it into their application. I don't believe the document for their API is public yet, so we don't know what the final interface will look like, but it's likely to be a simple REST API. In the future, I imagine your developers can take advantage of their API, or alternatively there will be community-made scripts for you to use/copy.
The pricing for using their API is explained here. Note that they charge per token, which might be important in case your game plans to make live calls to GPT-3 during gameplay (as opposed to mining a huge corpus of answers to build an offline database).
The use cases of GPT-3 suggests that you can legally use them for commercial products, although I couldn't find a definitive license or user agreement document.